There is a number of applications where it is necessary to measure currents across a high dynamic range with a good signal to noise ratio. For example, in isotope-ratio mass spectrometry, there is a need for an amplifier with the ability to respond accurately to signals with a high dynamic range and measure isotopic abundance with high precision. In such an application, a particularly demanding requirement occurs quite frequently. The amplifier must first measure a relatively large ion-current. This input signal fades out quickly and a few seconds later a relatively very weak second ion-current occurs (caused by a small isotopic abundance). The amplifier must be able to handle both the fast fade-out of the first signal and make a precise measurement of the relatively weak current signal.
In order to achieve this, the amplifier needs to have a fast and precise decay to zero (i.e. to the noise floor) after measuring the first signal almost to saturation of the amplifier. The amplifier also needs to generate minimal under-shoot and over-shoot of the output signal, even in the millivolt output range close to the noise floor of the amplifier.
Measurements of this type may be performed using transimpedance amplifiers, which are used to perform current to voltage conversion (‘transimpedance’).
FIG. 1 shows an example prior art transimpedance amplifier 100 comprising an operational amplifier 10 and a feedback resistor R that is connected between the inverting input of the operational amplifier 10 and the output of the operational amplifier 10. In an ideal case, the transimpedance amplifier will amplify the input current I and convert it into a low impedance output voltage V in accordance with the equation:V=−I*R 
Transimpedance amplifiers that are configured to operate with small or very small input currents I in the pico- to femto-ampere range typically operate with a large feedback resistor R in the range of 1E9 to 1E14 ohms.
When a very small input current I is being measured, a very small current flows through the feedback resistor R and produces a small voltage drop across the feedback resistor R, driving the negative input terminal of the operational amplifier 10 so that the output voltage V changes as a response to the input signal I. The output voltage V of the amplifier 100 is compensating the input voltage by the feedback resistor and drives the input terminal of the operational amplifier 10 to zero volts. An ideal amplifier will always preserve zero volts between its two input terminals.
In practice, however, a bias current is always superimposed on the measured input current I. If the bias current is constant an also constant voltage drop is present. For example, a bias current of 1 fA will cause a voltage drop of 10 mV when using a feedback resistor R of 10 TΩ. Ideally, this additional voltage drop should be as small as possible, which requires the selection of an operational amplifier 10 with a very small bias current.
When designing a transimpedance amplifier of this type, careful attention should be paid to its stability because extremely high impedance resistors exhibit a self-capacitance that tends to cause the amplifier to oscillate. In practice, it is known to limit the theoretical bandwidth of the amplifier by shunting the feedback resistor R with a small capacitor C in the range of 0.05-0.1 pF. The time-constant T of the feedback resistor R itself is then equal to T=R*C, which is approximately 0.5 to 1 second for very high value feedback resistors.
Where the amplifier 10 is required to achieve high precision measurement, for example around 1 ppm (part-per-million) in isotope-ratio mass spectrometry, the inherent exponential decay of the feedback resistor R at this precision equals a delay D of:D=ln(1E+6)*T=13.8*T=approximately 7 to 14 s.
A delay of this size might be reasonable for practical experiments, but due to the nature of extremely high impedance resistors and the added capacitor, such ideal parts in practice are not achievable. Most discrete electronic capacitors have a solid dielectric inside and non-ideal behaviors of the dielectric, such as finite insulation resistance (leakage current) and polarization effects (dielectric absorption), exclude the use of those capacitors.
The properties of extremely high impedance resistors in the tera-ohm range also differ considerably from ideal resistors. Temperature coefficient, voltage coefficient, self-capacitance and self-inductance have to be taken into account. The first two properties may be optimized by good material selection during manufacture and the last property may effectively be ignored due to the low speed of operation. However, self-capacitance should be treated very carefully in order to build a working amplifier.
One known technique for trying to compensate for the drawbacks associated with an ultra-high impedance resistor in a transimpedance amplifier is described, for example, in GB2393865B, wherein a lower value resistor is put in series with the ultra-high value resistor. The current to be measured is fed into the much lower impedance resistor and produces a compensation voltage drop to improve performance of current amplifiers.
However, this solution assumes a nearly ideal resistor model with only stray capacitance.
FIG. 2 shows the construction of an example ultra-high value resistor 200. The resistor 200 is constructed by coiling a high impedance resistive coating 220 around an insulative ceramic cylinder 210. The resistive coating 220 acts as the resistive element of the resistor 200 and the more helical spirals that are made, the more resistance the component exhibits. In order to protect the resistive element 220 from mechanical and/or chemical interference, the resistive element 220 is hermetically sealed with a lacquer coating 230, which may have a thickness of about 0.75 mm thickness, for example a thickness of between 0.5 mm-1 mm, such as 0.5 mm, 0.6 mm, 0.75 mm, 0.8 mm or 1 mm.
Theoretically, the lacquer coating 230 itself also acts as a resistive part because every layer has a finite resistance. Furthermore, because the layer is a good insulator, it also acts as a solid dielectric that can be polarized and that suffers from dielectric absorption. Therefore, the lacquer coating 230 may be treated as a distributed mesh of resistors and capacitors along the length of an ideal resistive component.
When measuring a small current, the distributed mesh of RC-networks acts as a shunt impedance. The value of the shunt impedance for ultrahigh value resistors can be very high, which results in a long charge-up duration of current being superimposed on the real current to be measured. Furthermore, the stored charges in the mesh will exhibit a fade out current even when the current to be measured is physically removed. In addition to this, electric fields surrounding the resistor will introduce charges in the mesh of RC-networks in the resistor coating. The effects together introduce a first exponential time constant to the transimpedance amplifier circuit, corrupting the slope of the measured rise and fall times and generally distorting amplifier response.
GB2424330A describes a technique for trying to overcome these problems by controlling the electric fields of the resistor. A metal cylinder is provided to surround the feedback resistor of a transimpedance amplifier and act as a capacitor that has air isolation and is held at a voltage equal to a fraction of the amplifier output voltage. Through this arrangement the sensitive feedback resistor is shielded and noise from external sources of electrical radiation and fields cannot disturb the signal. The transimpedance amplifier includes multiple operational amplifiers that are configured to improve gain and provide filter networks to achieve a minimal rise time of the amplifier.
In an alternative technique, U.S. Pat. No. 7,262,655B2 describes a transimpedance amplifier arrangement with a feedback resistor of a relatively low value of about 100KΩ. The feedback resistor is made up from a series of smaller value chip resistors. Each chip resistor is provided in close proximity with a low impedance counterpart in a parallel electrical resistor ladder, which is intended to compensate for the stray capacitance of the piecewise varying electrical field of the chip resistors.
However, the solutions suggested in GB2424330A and U.S. Pat. No. 7,262,655B2 assume that the feedback resistor is a constant linear device, which, in practice, is not the case for ultra-high value resistors. As a consequence, when an ultra-high value resistor is being used, the precision and repeatability of amplifier performance may be degraded.
Furthermore, with reference to the ultra-high value resistor 200 shown in FIG. 2, the insulative core 210 of the resistor 200 also acts as a dielectric and an axial electric field along the resistor body may cause a dielectric charge and therefore also dielectric absorption in the insulative core 210. Likewise, the insulative element 230 that surrounds the resistive element 220 may also suffer from dielectric absorption. This dielectric absorption introduces a second time constant, which results in a further unwanted delay and/or distortion when measuring very small currents (i.e. femto-ampere). In some cases, the second time constant can be so long that the output signal will effectively never reach the correct level (for example, OV) after a change in the input.
FIG. 3 shows an example response at the output of a transimpedance amplifier to a step change to a zero level signal at the input. This response demonstrates the effect of the first time constant, τ1, and the second time constant, τ2. The curve labelled τ1 shows the effect of τ1 when the feedback resistor is assumed to be a constant, linear device (i.e. the effect of τ2 is ignored). The curved labelled τ2 shows the real response of an amplifier with an ultra-high impedance feedback resistor. As can be seen, the dielectric absorption which introduced the second time constant has delayed and distorted the amplifier response, such that the amplifier output may effectively never reach the correct level.
FIG. 4 shows a further example amplifier response to a step change to a zero level signal at the input that may be typical of prior art transimpedance amplifiers. As can be seen, the amplifier output initially decreases quickly, because the amplifier is optimized to minimize τ1 and, therefore, have a fast initial response. However, after the fast initial response, a gradual creep in the output towards the final output level can be observed. This creep is caused by τ2, and causes a delay and distortion in the amplifier response, such that the amplifier output may effectively never reach the correct level.
These effects are highly significant for ultrahigh value resistors (i.e. 1 TΩ and above). Therefore, the solutions described in GB2424330A and U.S. Pat. No. 7,262,655B2 may be ineffectual for the measurement of very small currents using an ultrahigh impedance resistor.